We have that the measure of an external angle in a triangle is the sum of the non-adjacent angles to this external angle. Then, we have that:
[tex](2x+17)+(2x+20)=(7x+10)[/tex]
And now, we can solve this equation by summing like terms. Then, we have:
[tex]2x+2x+17+20=7x+10\Rightarrow4x+37=7x+10[/tex]
We need to subtract 4x to both sides of the equation:
[tex]4x-4x+37=7x-4x+10\Rightarrow0+37=3x+10[/tex]
Now, subtract 10 from both sides of the equation:
[tex]37-10=3x+10-10\Rightarrow27=3x+0\Rightarrow3x=27[/tex]
Divide both sides of the equation by 3:
[tex]\frac{3x}{3}=\frac{27}{3}\Rightarrow x=9[/tex]
And we have the value for x. However, we need to find the value for m< VWX = (7x+10). We need to plug the value of x in this equation. Then, we have:
[tex]m\angle VWX=(7\cdot9+10)=63+10=73\Rightarrow m\angle VWX=73[/tex]
Hence, the value for m
